$(3-4i)(a+bi)=25\qquad\text{use FOIL method}\\\\(3)(a)+(3bi)+(-4i)(a)+(-4i)(bi)=25+0i\\\\3a+3bi-4ai-4bi^2=25+0i\\\\3a+3bi-4ai-4b(-1)=25+0i\\\\3a+3bi-4ai+4b=25+0i\\\\(3a+4b)+(3b-4a)i=25+0i\\.\qquad\qquad\qquad\qquad\Downarrow\\\\3a+4b=25\ and\ 3b-4a=0\\\\3b-4a=0\qquad\text{add 4a to both sides}\\\\3b=4a\qquad\text{divide both sides by 3}\\\\b=\dfrac{4}{3}a\qquad\text{substitute it to the first equation}\\\\3a+4\left(\dfrac{4}{3}a\right)=25\\\\3a+\dfrac{16}{3}a=25\qquad\text{multiply both sides by 3}$

$9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}$

6 0

2 years ago

What is 2 plus 2 add 14 subtract 6

olasank [31]

What is 2 plus 2 add 14 subtract 6

2+2+14-6=

3 0

2 years ago

Read 2 more answers

(24.7C) The area of a rectangle is equal to x2 +

ss7ja [257]

Answer:

x + 5

Step-by-step explanation:

A = LW

W = A/L

W = (x^2 + 16x + 55)/(x + 11)

W = [(x + 11)(x + 5)]/(x + 11)

W = x + 5

3 0

2 years ago

the shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle?

balu736 [363]

I found the accompanying picture of this word problem.

The circle was inscribe in the triangle. The area outside of the circle but inside the triangle is the shaded area.

True. The shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle.

7 0

3 years ago